DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

Article in press


Authors:

M. Shahsavaran and M.R. Darafsheh

Title:

On semisymmetric cubic graphs of order $20p^2$, $p$ prime

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-10-08, Revised: 2019-02-26, Accepted: 2019-03-05, https://doi.org/10.7151/dmgt.2213

Abstract:

A simple graph is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let $p$ be an arbitrary prime. Folkman proved [Regular line-symmetric graphs, J. Combin. Theory 3 (1967) 215–232] that there is no semisymmetric graph of order $2p$ or $2p^2$. In this paper an extension of his result in the case of cubic graphs of order $20p^2$ is given. We prove that there is no connected cubic semisymmetric graph of order $20p^2$ or, equivalently, that every connected cubic edge-transitive graph of order $20p^2$ is necessarily symmetric.

Keywords:

edge-transitive graph, vertex-transitive graph, semisymmetric graph, order of a graph, classification of cubic semisymmetric graphs

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